Finite Group Databasebeta

← C31×#18791 #21475550

Subgroups — C31×#18791 #21475550

Order 7936.

938 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3480C211yesmaximal, characteristic
2C31×#3206C211yesmaximal, characteristic, complemented
3C31×#3079C211yesmaximal, characteristic, complemented
4C2×C31×#477C211yesmaximal, characteristic, complemented
5C31×#1638C212yesmaximal, complemented
6C31×#1636C212yesmaximal, complemented
7C31×#1631C212yesmaximal, complemented
8C31×#1630C212yesmaximal, complemented
9C31×#1547C211yesmaximal, characteristic, complemented
10C31×#1487C211yesmaximal, characteristic, complemented
11C31×#1477C211yesmaximal, characteristic, complemented
12C31×#559—21no—
13C31×#559C2211yescharacteristic
14C31×#557C2211yescharacteristic
15C31×#556—21no—
16C31×#556C2211yescharacteristic
17C31×#553—22no—
18C31×#553—21no—
19C31×#550C2211yescharacteristic
20C31×#548—21no—
21C31×#532—21no—
22C31×#532C2211yescharacteristic
23C2×C31×C4⋊Q8C2211yescharacteristic
24C31×#529—21no—
25C31×#529—22no—
26C4×#41×C31—21no—
27C4×#41×C31—21no—
28C4×#41×C31C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C31×#492C2212yes—
31C31×#487C2212yes—
32C31×#477—21no—
33C31×#477—21no—
34C31×#477C2212yes—
35C31×#477C2212yes—
36C31×#477C2212yes—
37C31×#476C2212yes—
38C31×#475—21no—
39C31×#474—21no—
40C31×#461—22no—
41C31×#448—22no—
42C31×#431C2211yescharacteristic
43C31×#428—21no—
44C2×C31×#107—21no—
45C31×#423C2211yescharacteristic
46C2×C31×C4⋊C8C2211yescharacteristic
47C31×#417—21no—
48C2×C31×#103—21no—
49C31×#332C2212yes—
50C31×#331C2212yes—
51C31×Q8⋊C8C2212yes—
52C31×Q8⋊C8C2212yes—
53C31×Q8⋊C8C2212yes—
54C31×D4⋊C8C2212yes—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31D411yescharacteristic
58C22×Q8×C31—21no—
59C22×Q8×C31D411yescharacteristic
60C2×SD16×C31—24no—
61C2×M16×C31—21no—
62C22×C8×C31—21no—
63C31×C4⋊Q8—21no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8C2312yes—
68C31×C4⋊Q8C2311yescharacteristic
69C31×#127—21no—
70C31×#127C2311yescharacteristic
71C31×#126—22no—
72C31×#126—22no—
73C31×#126—22no—
74C31×#125—22no—
75C31×#125—21no—
76C31×#124—22no—
77C31×#124—21no—
78C31×#124—21no—
79C31×#124—21no—
80C31×#124—21no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8—21no—
86C31×#121—22no—
87C31×#121—22no—
88C31×#121—22no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121D412yes—
92C4×Q8×C31—21no—
93C4×Q8×C31—21no—
94C4×Q8×C31—21no—
95C4×Q8×C31—21no—
96C4×Q8×C31—21no—
97C4×Q8×C31D411yescharacteristic
98C4×Q8×C31D411yescharacteristic
99C4×Q8×C31D411yescharacteristic
100C4×Q8×C31C2311yescharacteristic
101C4×Q8×C31C2311yescharacteristic
102C4×Q8×C31C2311yescharacteristic
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C4×D4×C31—22no—
107C4×D4×C31—22no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31D412yes—
115C4×D4×C31D411yescharacteristic
116C4×D4×C31C2311yescharacteristic
117C31×#117—22no—
118C31×#117—22no—
119C31×#117—21no—
120C31×#117—21no—
121C31×#117D411yescharacteristic
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31D411yescharacteristic
126C2×C42×C31—22no—
127C2×C42×C31—21no—
128C2×C42×C31—21no—
129C2×C42×C31C2311yescharacteristic
130C31×#107—22no—
131C31×#107—22no—
132C31×#107—22no—
133C31×#106—22no—
134C31×C4⋊C8—21no—
135C31×C4⋊C8—21no—
136C31×C4⋊C8—21no—
137C31×C4⋊C8C2312yes—
138C31×C4⋊C8C2312yes—
139C31×#103—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—24no—
143C31×#102—22no—
144C31×C22⋊C8—21no—
145C4×C8×C31C2312yes—
146#41×C31—22no—
147#41×C31—22no—
148#41×C31—42no—
149#41×C31—42no—
150#41×C31—42no—
151#41×C31—42no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—22no—
155C2×Q8×C31—22no—
156C2×Q8×C31—41no—
157C2×Q8×C31—41no—
158C2×Q8×C31—82no—
159C2×Q8×C31C2×D411yescharacteristic
160C2×Q8×C31C2×D411yescharacteristic
161C2×Q8×C31C2×D411yescharacteristic
162C2×D4×C31—22no—
163C2×D4×C31—21no—
164C2×D4×C31—22no—
165C2×D4×C31—22no—
166C2×D4×C31—21no—
167C2×D4×C31—21no—
168C2×D4×C31C2×D411yescharacteristic
169C2×D4×C31C2×D412yes—
170C22×C4×C31—22no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—41no—
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2×D411yescharacteristic
182SD16×C31—84no—
183M16×C31—42no—
184C2×C8×C31—22no—
185C2×C8×C31—22no—
186C2×C8×C31—22no—
187C2×C8×C31—42no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—22no—
190C4⋊C4×C31—22no—
191C4⋊C4×C31—22no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—22no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—41no—
203C4⋊C4×C31—41no—
204C4⋊C4×C31C2×D412yes—
205C4⋊C4×C31C2×D411yescharacteristic
206C4⋊C4×C31C2×D411yescharacteristic
207C4⋊C4×C31C2×D411yescharacteristic
208C4⋊C4×C31C2×D411yescharacteristic
209C22⋊C4×C31—22no—
210C22⋊C4×C31—22no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—22no—
213C22⋊C4×C31—22no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—21no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—21no—
220C42×C31—22no—
221C42×C31—22no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31C2×D411yescharacteristic
230C42×C31C2×D411yescharacteristic
231C42×C31C2×D411yescharacteristic
232C42×C31C2411yescharacteristic
233#18791C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—21no—
235C23×C31—22no—
236C23×C31#12011yescharacteristic
237Q8×C31—21no—
238Q8×C31—21no—
239Q8×C31—21no—
240Q8×C31—21no—
241Q8×C31—21no—
242Q8×C31—42no—
243Q8×C31—44no—
244Q8×C31—41no—
245Q8×C31—41no—
246Q8×C31—82no—
247Q8×C31#13712yes—
248D4×C31—21no—
249D4×C31—21no—
250D4×C31—42no—
251D4×C31—44no—
252D4×C31—42no—
253D4×C31—44no—
254D4×C31—41no—
255D4×C31—41no—
256D4×C31—41no—
257D4×C31—41no—
258D4×C31—82no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—22no—
268C2×C4×C31—21no—
269C2×C4×C31—41no—
270C2×C4×C31—42no—
271C2×C4×C31—44no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—42no—
275C2×C4×C31—44no—
276C2×C4×C31—42no—
277C2×C4×C31—81no—
278C2×C4×C31—81no—
279C2×C4×C31—82no—
280C2×C4×C31—82no—
281C2×C4×C31#12011yescharacteristic
282C2×C4×C31#12011yescharacteristic
283C2×C4×C31#12011yescharacteristic
284C2×C4×C31#13512yes—
285C2×C4×C31#13712yes—
286C2×C4×C31C22×D411yescharacteristic
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C22×D411yescharacteristic
289C8×C31—42no—
290C8×C31—42no—
291C8×C31—42no—
292#3480C2×C3111yescharacteristic
293#3206C2×C3111yescharacteristic, complemented
294#3079C2×C3111yescharacteristic, complemented
295C2×#477C2×C3111yescharacteristic, complemented
296#1638C2×C3112yescomplemented
297#1636C2×C3112yescomplemented
298#1631C2×C3112yescomplemented
299#1630C2×C3112yescomplemented
300#1547C2×C3111yescharacteristic, complemented
301#1487C2×C3111yescharacteristic, complemented
302#1477C2×C3111yescharacteristic, complemented
303C22×C31—21no—
304C22×C31—21no—
305C22×C31—41no—
306C22×C31—42no—
307C22×C31—42no—
308C22×C31—41no—
309C22×C31—42no—
310C22×C31—41no—
311C22×C31#45212yes—
312C22×C31C2×#12011yescharacteristic
313C4×C31—21no—
314C4×C31—22no—
315C4×C31—21no—
316C4×C31—21no—
317C4×C31—41no—
318C4×C31—42no—
319C4×C31—41no—
320C4×C31—41no—
321C4×C31—41no—
322C4×C31—41no—
323C4×C31—41no—
324C4×C31—82no—
325C4×C31#45212yes—
326C4×C31C2×#13511yescharacteristic
327C4×C31C2×#13711yescharacteristic
328C4×C31C2×#13711yescharacteristic
329C4×C31#57511yescharacteristic
330#559—21no—
331#559C22×C3111yescharacteristic
332#557C22×C3111yescharacteristic
333#556—21no—
334#556C22×C3111yescharacteristic
335#553—22no—
336#553—21no—
337#550C22×C3111yescharacteristic
338#548—21no—
339#532—21no—
340#532C22×C3111yescharacteristic
341C2×C4⋊Q8C22×C3111yescharacteristic
342#529—21no—
343#529—22no—
344C4×#41—21no—
345C4×#41—21no—
346C4×#41C22×C3111yescharacteristic
347C2×C4×Q8C22×C3111yescharacteristic
348#492C22×C3112yes—
349#487C22×C3112yes—
350#477—21no—
351#477—21no—
352#477C22×C3112yes—
353#477C22×C3112yes—
354#477C22×C3112yes—
355#476C22×C3112yes—
356#475—21no—
357#474—21no—
358#461—22no—
359#448—22no—
360#431C22×C3111yescharacteristic
361#428—21no—
362C2×#107—21no—
363#423C22×C3111yescharacteristic
364C2×C4⋊C8C22×C3111yescharacteristic
365#417—21no—
366C2×#103—21no—
367#332C22×C3112yes—
368#331C22×C3112yes—
369Q8⋊C8C22×C3112yes—
370Q8⋊C8C22×C3112yes—
371Q8⋊C8C22×C3112yes—
372D4⋊C8C22×C3112yes—
373C2×C31—22no—
374C2×C31—81no—
375C2×C31—82no—
376C2×C31C2×#45211yescharacteristic
377C2×C31#300711yescharacteristic
378C2×C31#302111yescharacteristic
379C2×#41—21no—
380C2×#41—21no—
381C2×#41D4×C3111yescharacteristic
382C22×Q8—21no—
383C22×Q8D4×C3111yescharacteristic
384C2×SD16—24no—
385C2×M16—21no—
386C22×C8—21no—
387C4⋊Q8—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8C23×C3112yes—
392C4⋊Q8C23×C3111yescharacteristic
393#127—21no—
394#127C23×C3111yescharacteristic
395#126—22no—
396#126—22no—
397#126—22no—
398#125—22no—
399#125—21no—
400#124—22no—
401#124—21no—
402#124—21no—
403#124—21no—
404#124—21no—
405#123—22no—
406#123—22no—
407#123—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410#121—22no—
411#121—22no—
412#121—22no—
413#121—21no—
414#121—21no—
415#121D4×C3112yes—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8—21no—
420C4×Q8—21no—
421C4×Q8D4×C3111yescharacteristic
422C4×Q8D4×C3111yescharacteristic
423C4×Q8D4×C3111yescharacteristic
424C4×Q8C23×C3111yescharacteristic
425C4×Q8C23×C3111yescharacteristic
426C4×Q8C23×C3111yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4—21no—
435C4×D4—21no—
436C4×D4—21no—
437C4×D4—21no—
438C4×D4D4×C3111yescharacteristic
439C4×D4D4×C3112yes—
440C4×D4C23×C3111yescharacteristic
441#117—22no—
442#117—22no—
443#117—21no—
444#117—21no—
445#117D4×C3111yescharacteristic
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4D4×C3111yescharacteristic
450C2×C42—22no—
451C2×C42—21no—
452C2×C42—21no—
453C2×C42C23×C3111yescharacteristic
454#107—22no—
455#107—22no—
456#107—22no—
457#106—22no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8C23×C3112yes—
462C4⋊C8C23×C3112yes—
463#103—22no—
464#103—22no—
465#103—22no—
466#103—24no—
467#102—22no—
468C22⋊C8—21no—
469C4×C8C23×C3112yes—
470C31#1879111yescharacteristic, direct product factor, Sylow
471#41—22no—
472#41—22no—
473#41—42no—
474#41—42no—
475#41—42no—
476#41—42no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—41no—
482C2×Q8—41no—
483C2×Q8—82no—
484C2×Q8C2×D4×C3111yescharacteristic
485C2×Q8C2×D4×C3111yescharacteristic
486C2×Q8C2×D4×C3111yescharacteristic
487C2×D4—22no—
488C2×D4—21no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4C2×D4×C3111yescharacteristic
494C2×D4C2×D4×C3112yes—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—41no—
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507SD16—84no—
508M16—42no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—42no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4C2×D4×C3112yes—
530C4⋊C4C2×D4×C3111yescharacteristic
531C4⋊C4C2×D4×C3111yescharacteristic
532C4⋊C4C2×D4×C3111yescharacteristic
533C4⋊C4C2×D4×C3111yescharacteristic
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—21no—
541C22⋊C4—22no—
542C22⋊C4—21no—
543C22⋊C4—22no—
544C22⋊C4—21no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42C2×D4×C3111yescharacteristic
555C42C2×D4×C3111yescharacteristic
556C42C2×D4×C3111yescharacteristic
557C42C24×C3111yescharacteristic
558C23—21no—
559C23—22no—
560C23C31×#12011yescharacteristic
561Q8—21no—
562Q8—21no—
563Q8—21no—
564Q8—21no—
565Q8—21no—
566Q8—42no—
567Q8—44no—
568Q8—41no—
569Q8—41no—
570Q8—82no—
571Q8C31×#13712yes—
572D4—21no—
573D4—21no—
574D4—42no—
575D4—44no—
576D4—42no—
577D4—44no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—41no—
582D4—82no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—81no—
602C2×C4—81no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4C31×#12011yescharacteristic
606C2×C4C31×#12011yescharacteristic
607C2×C4C31×#12011yescharacteristic
608C2×C4C31×#13512yes—
609C2×C4C31×#13712yes—
610C2×C4C22×D4×C3111yescharacteristic
611C2×C4C22×D4×C3111yescharacteristic
612C2×C4C22×D4×C3111yescharacteristic
613C8—42no—
614C8—42no—
615C8—42no—
616C22—21no—
617C22—21no—
618C22—41no—
619C22—42no—
620C22—42no—
621C22—41no—
622C22—42no—
623C22—41no—
624C22C31×#45212yes—
625C22C2×C31×#12011yescharacteristic
626C4—21no—
627C4—22no—
628C4—21no—
629C4—21no—
630C4—41no—
631C4—42no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—82no—
638C4C31×#45212yes—
639C4C2×C31×#13511yescharacteristic
640C4C2×C31×#13711yescharacteristic
641C4C2×C31×#13711yescharacteristic
642C4C31×#57511yescharacteristic
643C2—22no—
644C2—81no—
645C2—82no—
646C2C2×C31×#45211yescharacteristic
647C2C31×#300711yescharacteristic
648C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3480C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#3206C2semidirect
3. C31×#3079C2semidirect
4. C2×C31×#477C2semidirect
5. C31×#1638C2semidirect
6. C31×#1636C2semidirect
7. C31×#1631C2semidirect
8. C31×#1630C2semidirect
9. C31×#1547C2semidirect
10. C31×#1487C2semidirect
11. C31×#1477C2semidirect
233. #18791C31direct (N × H)
293. #3206C2×C31semidirect
294. #3079C2×C31semidirect
295. C2×#477C2×C31semidirect
296. #1638C2×C31semidirect
297. #1636C2×C31semidirect
298. #1631C2×C31semidirect
299. #1630C2×C31semidirect
300. #1547C2×C31semidirect
301. #1487C2×C31semidirect
302. #1477C2×C31semidirect
470. C31#18791direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#34802
C31×#32062
C31×#30792
C2×C31×#4772
C31×#16382
C31×#16362
C31×#16312
C31×#16302
C31×#15472
C31×#14872
C31×#14772
#1879131